You, Ada, and Carlos are on a game show where the host will ask contestants to wager money. Assume that Ada and Carlos are very smart, and that each of you will be willing to wager money if and only if there is a greater than 50% chance you will win that wager. The three of you each roll a 12-sided die (numbered 1 to 12) and keep your result private.

-The host asks Ada: "Would you like to wager $1 that your number is higher than or equal to Carlos's?" -Ada says: "No" -The host asks Carlos: "Would you like to wager $1 that your number is higher than or equal to Ada's?" -Carlos says: "Yes" -The host asks you: "Would you like to wager $1 that your number is higher than or equal to Carlos's?" You rolled an 8.

a. Assuming that Carlos heard Ada's conversation with the host, should you make the wager? If you did make it, what is the probability that you would win? Why? b. What if you think that Carlos did not hear Ada's conversation before giving his response. Now should you make the wager? What is the probability that you would win? c. How certain do you need to be that Carlos heard Ada's conversation for you to make the wager?